Contact ton Pairing of the Perchlorate Ion
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Contact Ion Pairing of the Perchlorate Ion. A Chlorine-35 Nuclear Magnetic Resonance Study. 1. Solutions in Pure Solvents Harvey Alan Berman and Thomas R. Stengle. Department of Chemistty, University of Massachusetts, Amherst, Massachusetts 0 1002 (Received September 5, 1974)
The NMR relaxation time (2’2) of the 35Cl nucleus has been used to study the ion pairing behavior of the perchlorate ion. Free Clod- in solution has a long relaxation time compared with a perchlorate ion in a contact ion pair. This is caused by quadrupolar relaxation, and it is observed by its effect on the NMR line width. The tendency of c104- to form contact ion pairs has been studied as a function of cation and solvent. Factors favoring contact ion pairing are high charge to radius ratio of cation, low dielectric constant of solvent, and low basic strength (measured by Gutmann’s donor number) of solvent.
Introduction Electrolytes in solution often exist as complex mixtures of several species: solvated ions, solvent-separated ion pairs, contact ion pairs, and more complex ion aggregates. Since the rates of chemical reactions are often affected by the state of aggregation of ions, it is important to have an understanding of the equilibrium among the many ionic species. A host of experimental methods has been developed to study ion ass0ciation.l Electrical conductivity is an obvious approach, and it has been used to study a wide variety of solutions. However, this technique fails to distinguish between contact and solvent-separated ion association. In fact, this is a difficult distinction to make, and many of the classical methods fail a t this point. To solve this problem it is necessary to study a parameter which is sensitive to the short range interactions between ions in intimate contact. Spectroscopic methods have proven to be a fruitful approach here. The infrared and Raman spectra of polyatomic ions have been used to detect ion pair formation.2 Recently nuclear magnetic resonance techniques have been developed to deal with the problem. For example, the NMR signal of a diamagnetic ion is affected by the presence of a paramagnetic counterion. The interaction is short ranged, and its effect has been used to study a number of systems? In purely diamagnetic solutions, chemical shift methods can be used. The 23Nachemical shift is sensitive to contact ion pairing: and this technique has been widely applied. Here we report an NMR method based on the relaxation time of the 35Cl nucleus in the perchlorate ion. This parameter is easily measured, and it reveals the presence of contact ion pairs, while it is insensitive to solvent-separated ion aggregation. In the 35Cl nucleus the interaction of the nuclear electric quadrupole moment with an electric field gradient provides an efficient mechanism of relaxation! In almost every situation this mechanism predominates, and other relaxation pathways can be ignored. In the liquid state the extreme narrowing conditions apply, and the relaxation rates are given by
for a nucleus of spin Z = 3h. Here 7 is the asymmetry parameter, Q is the nuclear quadrupole moment, q is the elec-
tric field gradient at the nucleus, and T~ is the correlation time for molecular reorientation. If the environment of the chlorine nucleus has cylinderical symmetry, the asymmetry parameter is zero. Relaxation times are especially sensitive to the electric field gradient, q. This field arises from the distribution of charge around the nucleus, Le., the surrounding electrons and nearby nuclei. If a counterion comes into contact with a Clod-, a large field gradient will be generated at the chlorine nucleus, and the relaxation rate will be greatly enhanced. In our observations the shape of the 35Cl resonance has been lorentzian. This implies that the relaxation rate is related to the line width by AV = l/nTz
(2 )
where AU is the full width of the NMR line at half height. This relation affords a convenient method of measuring relaxation times, and it is customary to report data as line widths in hertz rather than as the relaxation times themselves. The field gradient at the chlorine nucleus in the free gaseous perchlorate ion is zero because of the tetrahedral symmetry. When the ion is in solution, its solvation shell will not possess such high symmetry, and a small fluctuating field gradient will be generated. The gradient will not be large, because solvent molecules are disposed about the ion in a way which is approximately symmetrical. In solution the free clod- gives a 35Clsignal which is only a few hertz wide.6 The close approach of a counterion destroys the approximate symmetry of the solvation shell and generates a large field gradient at the chlorine nucleus. The result is a large 35Cl line width when the Clod- is in contact with a counterion. It is not uncommon for the line width to increase by a factor of 100 upon formation of contact ion pairs. The magnitude of the field gradient due to the counterion is strongly dependent on interionic distance; therefore, solvent-separated ion pairs yield a line broadening that is negligible when compared with the effect of ions in contact. These conclusions are borne out by a calculation based on a simple electrostatic model (cf. Discussion). In extremely dilute solutions of perchlorate salts it is safe to assume that all of the C104- is free; the line width will be a few hertz due to ion-solvent interactions. In a more concentrated solution, contact ion pairs may form which will produce large line widths. Contact ion pairing The Journal of Physical Chemistry. Vol. 79, No. IO, 1975
H. A. Berman and T. R. Stengle
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can be detected by examining the line width as a function of concentration. Unfortunately the sensitivity of the NMR experiment is low, and it is often not possible to obtain spectra a t concentrations where only free ions are present. In such cases the line widths of concentrated solutions must be compared with data from solvents in which it is certain that contact ion pairs do not exist. In making comparisons from one solvent to another (or from one concentration to another in the same solvent) we are primarily concerned with changes in the field gradient, q. However, changes in the correlation time will also affect the line width; a change in T~ will tend to obscure the effect of a change in q. It is desirable to express the line width data in terms of a parameter which reflects changes in q without being affected by changes of rc. It is not possible to accomplish this rigorously, but an approximate quantity can be derived from a simple model. If rc is governed by the same factors which influence a sphere turning in a viscous liquid, it will be proportional to the viscosity of the s o h t i ~ n The . ~ effect of T~ will be removed if the line width is divided by the viscosity. This approach seems to be valid for some simple system^,^,^ but there are cases where the macroscopic viscosity does not accurately reflect changes in T,.9,10 In concentrated solutions, or in solutions of macromolecules, there is no clear way to separate the effects of rc and q. In moderately concentrated salt solutions there can exist a number of distinct species which are in facile equilibrium with each other. Since the lifetime of an ion aggregate is short compared with the NMR time scale, only a single signal is observed. The relaxation time is the average of the relaxation times of the individual species weighted by their concentrations
where T Z is the observed relaxation time, x i is the mole fraction of c104- present in species i, and 2‘2; is the relaxation time in that species.
Experimental Section Materials. All salts and solvents were of the highest purity available. The perchlorate salts were obtained from G. Frederick Smith Chemical Co., and they were used without further purification except for drying. Acetonitrile was purified and dried by a standard procedure;l’ ethanol was dried by distillation from magnesium turnings and iodine under nitrogen. The solvents were stored over molecular sieves in dark bottles. The salt solutions were prepared directly before use by diluting a freshly prepared stock solution. A violent explosion occurred during the ‘preparation of a solution of Mg(C104)~in dimethyl sulfoxide at room temperature, and our results in this solvent are incomplete due to the hazardous nature of the system. The other perchlorate salts are also unstable in this solvent. N M R Measurements. The 35Clspectra were observed with a Varian DP instrument operating at 4.3 MHz. Signals which had a width of less than 300 Hz were recorded as absorption spectra, and the line width at half height was measured directly. Broader signals were recorded as the first derivative of the absorption mode. The line width was derived from the peak to peak distance, dpp, by assuming a lorentzian shape function, i.e., Au = d3dpp.Each measurement is the average of at least five determinations. The The Journal of Physical Chemistry, Vol. 79, No. 10, 1975
n
I
0 = Mg(CIO,),
A = LiCIO,
n=NaCIO,
0.0
0.5
1
1.0
Conc. (moles/liter) Figure 1. Line width of 35CIsignal divided by viscosity for solutions of perchlorate salts in acetonitrile as a function of concentration.
precision of the measurements varied with the width of the line in question. It ranged from 5% for line widths less than 500 Hz to 20% for line widths greater than 3000 Hz. The magnetic field inhomogeniety placed a lower limit of 5 Hz on the observed line width. In solutions containing only free perchlorate ion, the line width is expected to be quite small? and the inhomogeniety limit was observed. In such cases the line width is reported as
